alLearnMoreRel=paste0("<p>Determine the optimal number of clusters by inspecting ",

"the average silhouette width and the total within cluster sum of squares (WSS) ",

"for a range of cluster numbers.</p>",

"<p><b>Silhouette analysis</b> estimates the average distance between clusters. ",

"Larger silhouette widths indicate better.<p>",

"<p><b>Silhouette analysis</b> first computes how close each trajectory is with others in the cluster it is assigned to, ",

"this is then compared to closeness with trajectories in other clusters. ",

"Larger average silhouette widths usually indicate better clustering. To make sure averaging does not hide a locally bad",

"clustering, this should be inspected along with the silhouette plot in the \"Internal\" tab.<p>",

"<p><b>WSS</b> evaluates the compactness of clusters. ",

"Compact clusters achieve low WSS values. ",

"Look for the <i>knee</i> in the plot of WSS as function of cluster numbers.</p>"),

"Look for the <i>elbow</i> in the plot of WSS as function of cluster numbers.</p>"),

alLearnMoreInt=paste0("<p>Evaluate the goodness of a clustering structure by inspecting ",

"principle components, the dendrogram, ",

"principal components, the dendrogram, ",

"and the silhouette for a given number of clusters.</p>",

"<p>Each point in the scatter plot of 2 principle components corresponds to a single time series. ",

"<p><b>Principal components:</b> Each point in the scatter plot corresponds to a single time series in the first 2 PCs space. ",

"Points are coloured by cluster numbers. Compact, well separated clusters ",

"indicate good partitioning.</p>",

"<p>The height of dendrogram branches indicates how well clusters are separated.</p>",

"<p>The silhouette plot displays how close each time series in one cluster ",

"is to time series in the neighboring clusters. ",

"A large positive silhouette (Si) indicates time series that are well clustered.",

"A negative Si indicates time series that are closer to ",

"a neighboring cluster, and are placed in the wrong cluster.</p>")

"indicate good partitioning. The percentage of total variance carried by each PC is indicated.</p>",

"<p><b>Dendrogram:</b> The height of branches indicates how well clusters are separated.</p>",

"<p><b>Silhouette plot:</b> The plot indicates for each series whether it is on average closer to series within its cluster ",

"or to series in other clusters. Each bar represents the <a href=https://en.wikipedia.org/wiki/Silhouette_(clustering) title=\"External link\">silhouette score</a> ",

"(Si) for one series. The height of the bars varies ",

"between 1 (the series is much closer to series in its cluster) and -1 (the series is much closer to series in an other cluster). ",

"Hence, large positive values of Si are usually associated with better clustering, while negative values are associated with worse clustering.")